Q. 94.1( 35 Votes )

The first term of a G.P. is 1. The sum of the third term and fifth term is 90. Find the common ratio of G.P.

Answer :

Let a and r be the first term and the common ratio of the G.P. respectively.


a1 = 1


nth term of G.P is given by -


an = arn - 1


a3 = ar2 = (1)r2


a6 = ar4 = (1)r4


According to question -


a3 + a6 = 90


r2 + r4 = 90


r4 + r2 – 90 = 0


Assume r2 = t


t2 + t – 90 = 0


t2 + 10t - 9t – 90 = 0


t(t + 10) - 9(t + 10) = 0


(t - 9)(t + 10) = 0


t =9 or t = - 10(invalid because t = r2, so t can't be - ve.)


r2 = 9 ( Taking real roots)


r = 3


Thus, the common ratio of the G.P. is 3.


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